Subgroups — D₃₅×D₁₃₉ #34085643

Order 19460.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₈₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₅×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₁₃₉	—	5	1	no	maximal, Hall
6	D₅×D₁₃₉	—	7	1	no	maximal, Hall
7	D₉₇₃	—	5	1	no	—
8	C₇×D₁₃₉	D₅	1	1	yes	characteristic, complemented
9	D₇×C₁₃₉	—	5	1	no	—
10	D₆₉₅	—	7	1	no	—
11	C₅×D₁₃₉	D₇	1	1	yes	characteristic, complemented
12	D₅×C₁₃₉	—	7	1	no	—
13	C₇×C₁₃₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₃₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₃₉	—	35	1	no	Hall
16	C₂×C₁₃₉	—	35	1	no	—
17	D₁₃₉	—	35	1	no	—
18	D₁₃₉	D₃₅	1	1	yes	characteristic, direct product factor
19	C₂×D₃₅	—	139	1	no	maximal, Hall
20	C₁₃₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₅×C₇	—	139	1	no	—
22	D₃₅	—	139	1	no	—
23	D₃₅	D₁₃₉	1	1	yes	characteristic, direct product factor
24	C₅×C₇	C₂×D₁₃₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	695	1	no	Hall
26	C₂×D₅	—	973	1	no	Hall
27	C₂×C₇	—	139	1	no	—
28	D₇	—	5	1	no	—
29	D₇	—	695	1	no	—
30	C₂×C₅	—	139	1	no	—
31	D₅	—	7	1	no	—
32	D₅	—	973	1	no	—
33	C₇	D₅×D₁₃₉	1	1	yes	characteristic, complemented, Sylow
34	C₅	D₇×D₁₃₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	4865	1	no	Sylow
36	C₂	—	4865	1	no	—
37	C₂	—	35	1	no	—
38	C₂	—	139	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₃₉	C₂²
LCS	G ▷ C₅×C₇×C₁₃₉
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₄₈₆₅	C₂	semidirect
2. D₃₅×C₁₃₉	C₂	semidirect
3. C₅×C₇×D₁₃₉	C₂	semidirect
4. C₅×C₇×C₁₃₉	C₂²	semidirect
8. C₇×D₁₃₉	D₅	semidirect
11. C₅×D₁₃₉	D₇	semidirect
13. C₇×C₁₃₉	C₂×D₅	semidirect
14. C₅×C₁₃₉	C₂×D₇	semidirect
18. D₁₃₉	D₃₅	direct (N × H)
20. C₁₃₉	C₂×D₃₅	semidirect
23. D₃₅	D₁₃₉	direct (N × H)
24. C₅×C₇	C₂×D₁₃₉	semidirect
33. C₇	D₅×D₁₃₉	semidirect
34. C₅	D₇×D₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄₈₆₅	2
D₃₅×C₁₃₉	2
C₅×C₇×D₁₃₉	2
D₇×D₁₃₉	5
D₅×D₁₃₉	7
C₂×D₃₅	139

Subgroups — D35×D139 #34085643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅×D₁₃₉ #34085643